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Learning to Match Unpaired Data with Minimum Entropy Coupling
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Proposes DDMEC, a cooperative pair of conditional diffusion models that minimize joint entropy under soft marginal constraints to match unpaired continuous data, evaluated on single-cell multi-omics alignment and unpaired image translation.
Problem
Matching unpaired multimodal data by learning a joint distribution; existing minimum entropy coupling (MEC) methods handle only finite discrete distributions, while OT-based alternatives require geometric costs and comparable spaces.
Approach
Extends MEC to continuous distributions by parameterizing two specular conditional diffusion models (X|Y and Y|X) whose denoising-based log-likelihoods serve as rewards that cooperatively minimize conditional entropy, with KL terms keeping marginals close to pretrained unconditional models and the two joints consistent.
Key results
- On PBMC, DDMEC reaches 66.3% cell-type and 46.0% subcell-type neighborhood accuracy, above the best baseline scTopoGAN (61.7%, 41.3%).
- On CelebA-HQ Male->Female, DDMEC (50 steps, guidance=2) achieves FID 36.99 vs. best baseline EGSDE 41.93, and SSIM 0.593 at guidance 2.5 vs. 0.574.
- On AFHQ Cat->Dog, DDMEC (100 steps, guidance=7) attains FID 57.89, the best FID, but SSIM (0.397) is below CUT (0.601) and SDEdit (0.423).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DDMEC instead of the strongest reported baseline | Single-cell multi-omics alignment · PBMC | Celltype Acc: 61.7 ± 8.6 -> 66.3 ± 2.6 | Helped |
| Use DDMEC instead of the strongest reported baseline | Single-cell multi-omics alignment · PBMC | Subcelltype Acc: 41.3 ± 6.5 -> 46.0 ± 0.5 | Helped |
| Use DDMEC instead of SCOT | Single-cell multi-omics alignment · BM | Celltype Acc: 90.5 ± 0.0 -> 77.3±0.1 | Hurt |
| Use DDMEC instead of the strongest reported baseline | Single-cell multi-omics alignment · BM | Subcelltype Acc: 31.6 ± 0.0 -> 44.2±0.1 | Helped |
| Use DDMEC instead of MMD-MA | Single-cell multi-omics alignment · SNAREseq | FOS: 0.150 -> 0.147 | Helped |
| Use DDMEC instead of InfoOT | Single-cell multi-omics alignment · SNAREseq | Acc: 98.8 -> 98.6 | Hurt |
| Use DDMEC instead of the strongest reported baseline | Unpaired image translation · AFHQ Cat→Dog | FID: 54.88 ± 1.01 -> 57.89 ± 0.37 | Hurt |
| Increase guidance from 7 to 9 (ablation) | DDMEC · AFHQ Cat→Dog, 50 sampling steps | SSIM: 0.404 ± 0.001 -> 0.410 ± 0.001 | Helped |
| Increase guidance from 7 to 9 (ablation) | DDMEC · AFHQ Wild→Dog, 50 sampling steps | FID: 60.67 ± 1.01 -> 62.03 ± 1.18 | Hurt |
| Increase guidance from 7 to 9 (ablation) | DDMEC · AFHQ Wild→Dog, 50 sampling steps | SSIM: 0.353 ± 0.004 -> 0.360 ± 0.002 | Helped |
| Increase sampling steps from 50 to 100 (ablation) | DDMEC (guidance=7) · CelebA-HQ Male→Female | FID: 36.99± 0.83 -> 34.86 ± 0.70 | Helped |
| Increase guidance from 2 to 2.5 (ablation) | DDMEC · CelebA-HQ Male→Female, 50 sampling steps | SSIM: 0.556 ± 0.002 -> 0.593 ± 0.003 | Helped |
Surprising findings
- On BM, SCOT achieves higher cell-type accuracy (90.5) than DDMEC (77.3), so DDMEC is not consistently best across datasets.
- Higher guidance scale improves SSIM but worsens FID, a trade-off that is explicitly exposed in the image translation results.
Limitations
- On AFHQ, DDMEC is not best on SSIM for several tasks and is not best on BM cell-type alignment.
- Fine-tuning diffusion models with RL is computationally costly, as the paper notes for alternative methods; the approximation to the true MEC objective relies on cooperative swapping and a finite-capacity denoiser.
Experimental setup
Datasets: PBMC multiome bone marrow CITE-seq SNAREseq AFHQ CelebA-HQ
Benchmarks: PBMC BM SNAREseq AFHQ Cat->Dog AFHQ Wild->Dog CelebA-HQ Male->Female
Metrics: Celltype Acc Subcelltype Acc FOSCTTM label transfer accuracy FID SSIM
Baselines: SCOT MMD-MA UnionCom scTopoGAN InfoOT CycleGAN CUT StarGAN v2 SDEdit ILVR EGSDE SDDM
Builds on: DDPM classifier-free guidance denoising diffusion RL (DDPO) scTopoGAN EGSDE
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